(x - 4)(x + 3)
foil
y = x^2 - x - 12
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Answer t What is the slope of the line graphed below?his question…
So, if we have the equation: F(x) = x^2 + 3 this is a function in terms of x, another way to look at this same problem is to write it as: y= x^2 +3. This function may be graphed if that is what you are looking for, the graph will be of a parabola and then the graph will be shifted from the origin up 3 from the origin.
Whether or not a function has zeros depends on the domain over which it is defined.For example, the linear equation 2x = 3 has no zeros if the domain is the set of integers (whole numbers) but if you allow rational numbers then x = 1.5 is a zero.A quadratic function such as x^2 = 2 has no rational zeros, but it does have irrational zeros which are sqrt(2) and -sqrt(2).Similarly, a quadratic equation need not have real zeros. It will have zeros if the domain is extended to the complex field.In the coordinate plane, a quadratic without zeros will either be wholly above the horizontal axis or wholly below it.
The simplest example that fits that is y = x^2 - 7x + 12. A math professor wouldn't like the process, but assuming we want a positive quadratic, and since positive quadratics are symmetrical along their minimums, we can skip some steps. We know that the local minimum is going to lie exactly between 3 and 4, at x = 7/2. Put everything on one side to get 2x - 7 = 0. Taking the integral (and skipping a few more steps) gets y = x^2 - 7x + c. Solving for c where y = 0 when x = 3, we find c = 12.
x2 + 15x +36